# WWU MATH 113 - Section 5.4: Decimals, Exponents, and Real Numbers (16 pages)

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# Section 5.4: Decimals, Exponents, and Real Numbers

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## Section 5.4: Decimals, Exponents, and Real Numbers

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Lecture Notes

Pages:
16
School:
Walla Walla University
Course:
Math 113 - Mathematics for Elementary Teachers II
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Introduction Modeling with Decimals Irrational Numbers MATH 113 Section 5 4 Decimals Exponents and Real Numbers Prof Jonathan Duncan Walla Walla University Winter Quarter 2008 Conclusion Introduction Modeling with Decimals Outline 1 Introduction 2 Modeling with Decimals 3 Irrational Numbers 4 Conclusion Irrational Numbers Conclusion Introduction Modeling with Decimals Irrational Numbers Decimals Decimals are an even more recent invention than fractions History of Decimals In 1585 Flemish mathematician Simon Stevin published a small pamphlet La Thiende The Tenth in which he presented an account of decimal fractions and their daily use Though he did not invent decimal fractions and his notation was clumsy he established the use of decimals in day to day mathematics Decimal Notation To this day decimal notation varies United States 3 14 United Kingdom 3 14 Continental Europe 3 14 Conclusion Introduction Modeling with Decimals Irrational Numbers Decimals and Place Value In order to tie decimals into our existing number system we will start with an examination of place values Decimal Place Values In base 10 decimals have place values which are negative powers 1 of 10 or positive powers of 10 102 101 100 10 1 10 2 Example Suppose we used a base 5 system What would the decimal place values look like Conclusion Introduction Modeling with Decimals Irrational Numbers Decimals and Fractions As decimals were originally intended to simplify working with fractions there is a strong connection between the two concepts Decimals and Fractions Decimals are an alternative to fractions with denominators which 1 3 are powers of 10 For example 0 3 0 1 3 10 10 Example Convert each fraction to a decimal 1 2 1 4 1 16 1 3 Example Convert each decimal to a fraction 0 3 0 045 0 23 Conclusion Introduction Modeling with Decimals Irrational Numbers Conclusion The Importance of 0 Zero plays an important role in our numbering system This role is especially important when writing decimal numbers The

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